(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Integration of a natural log

I am asked to Integrate by parts

[tex]\int \ln(2x+1) dx[/tex]

So,

[tex]\mbox{u}=ln(2x+1)[/tex]

[tex]\mbox{du}=\frac{2}{2x+1}[/tex]

[tex]\mbox{dv}=\mbox{dx}[/tex]

[tex]\mbox{v}=\mbox{x}[/tex]

I plug all of that in and I get,

[tex]{\int \ln(2x+1) dx\}={\mbox{x}\ln(2x+1)}-{\int \frac{2x}{2x+1} \mbox{dx}}[/tex]

At this point I tried doing another substitution letting u equal 2x, but this just brought me back to the original question.

After this anything I try to do doesn't lead me anywhere. I know it can be solved because the answer is in the back of the book.

First, is what I have done so far correct?

Second, how do I finish the problem?

Any help you have would be greatly appreciated.

Erik

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# Homework Help: Integration of a natural log

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